Plants that are too shallow get heat stress faster, drought stress faster, and can get cold damage over the winter if that crown gets exposed. Deeper plants tend to stay dormant longer which can be important with frost sensitive plants like the fragrant ones. If you have hostas coming back smaller with smaller leaves, check if you can see the crown. If so it is too shallow.
Plants that are too deep will need to grow up closer to the surface. Eyes may emerge further out from where the main clump was located so that you no longer have a tight clump. Stems may rot a little easier if they get buried in summer by mulch.
I always try to get the "right" depth, but I would much rather err on the side of planting a little too deep. Plants will establish the "correct" depth the very next season if they were too deep. For example if you plant a crown at 3" and it wanted to be 2" you will probably never even notice that it had to grow up that extra inch below the surface before producing a new eye. However, plants can take several seasons to grow deeper if they come back at all when planted too shallow.
In our rows we will often find that the largest hostas are the ones that were planted a little deeper than the rest. TOO deeply and we will see that the eyes are spaced a little further apart but are still usually the largest plantlets. When we have a plant that is struggling we find that the crown is often right at or slightly below the surface. We also find that moles often tunnel underneath plants causing them to rise up closer to the surface, plus creating an air pocket under the plant. Those plants dry out in the summer and struggle over the winter.
The only time that depth may pose a problem is if they were buried or sank during the season. If a hosta was growing at a depth of 1" from the top of the eyes/dormant buds to the surface and was then planted at a depth of 3" you might get some stem rot. By early to mid summer most stems are hardened off to the soil and can tolerate a little covering but you might get rot problems during the heat of the summer. Because of this we prefer to topdress shallow hostas in the fall after they are starting to go dormant. In most cases it is just better to get the depth close when planting and the hosta will find its way the next spring if you were off a little.
Two examples of plants finding the right depth after being planted too deep:
1) A Hosta 'Riptide', one eye, was planted last summer with the crown at a depth of 3 1/2". This particular eye emerged last, but by mid summer the eye was slightly larger than other plants around it. I dug it up and it had grown an elongated stem out of the main eye and then established a new crown at a depth of 2", measured from the top of the dormant buds to the soil level. Roots were at about 2 1/4". Our remaining plants were only at a depth of about 1" but should have been planted up to 2" deep without causing any harm.
2) A Hosta 'Pineapple Juice' was noticed in the growing area with 6 eyes spaced very far apart. It was planted last fall. Upon digging it I noticed that it had been planted too deeply, and possibly at an angle. The deepest eye from last fall was at a depth of 4 1/2". The shallowest was at a depth of 1 1/2". All of the eyes produced elongated stems and every single one produced a new eye at a depth of 1 1/4" with roots around 1 1/2". So in this case the proper depth would have been about 1 1/4".
Here are pictures of the Pineapple Juice. It was 2 eyes planted last fall when dormant:
And here is a picture of what it looks like below the surface. Note the elongated stems that emerged from last year's dormant buds. Those stems grow up to the correct depth for this hosta and then develop new crowns.
Another picture of the side of the crown that was a little shallower, but still too deep.
Because this hosta had developed all new, separate, well rooted eyes I went ahead and divided off all the stems. I got 6 individual plants:
And finally, here is the leftover crown from last year after the divisions were taken off. There are a couple tiny dormant buds still on this crown. I replanted the crown at a depth of 1 1/4" to the top and it will probably grow a couple tiny babies next year:
After observing many plants I have discovered that every hosta wants to grow at a slightly different depth. Riptide was 2". Pinepple Juice was 1 1/4". And I've noticed on Kiwi Hippo, a giant hosta, that it did not develop any elongated stems even when eyes were 4" deep. It seems that the larger the plant and the larger the eyes the deeper they want to be. In all cases the dormant buds prefer to be completely buried.
I'm using this rule of thumb when planting new plants, based on the overall, mature plant size approximation. It may be closer related to mature eye size. The larger the eye the deeper the crown wants to be:
Mini - I plant about 1/2" deep (soil to top of buds)
Small - about 1/2 to 1" deep
Medium - about 1" to 1 1/2" deep
Large - about 1 1/2" to 2" deep
Giant - 2" to 3" deep
My advice: If you can see the dormant buds at the surface in the fall consider topdressing the crowns with organic matter so that they are better protected. An extra 1/2" of compost or an inch of shredded leaves could make a big difference in how well they come back the next year.
I hope that is helpful to see what happens when a hosta is planted "too" deep.
I was starting to wonder if I'd been doing it wrong these many years, what with all the advice going around to plant hosta crowns at the soil level like iris. Thanks for the reinforcement. 
We discussed this when I visited, but it's nice to have it written down so I don't have to try to remember all that you said. 
Great pics!! I always wondered why some varieties developed the elongated roots. Now I know. Thanks!! This would be another good addition to the FAQ.
